I hiked Hawaii for the first time this past Spring. And it’s been much on my mind since.
When can I get back for more?
My friends Lexi and Kelly hiked in Kauai this past year too. They very much liked Polihale State Park:
Also the Nualolo and Awaiawaipuhi trails:
We agreed that Hawaii can be VERY inexpensive. You only need a tent, a rent-a-car and hiking packs. Beach campsites in Kauai cost $3-5 / night.
My inexpensive lunch with a view:
besthike.com 
I lived on Kaua’i for three years in the late 1990s. I especially loved the hiking.
Polihale State Beach has many camping sites, or you can do what I did–sleep on the sand on an isolated part of the beach.
You give excellent advice on how to enjoy Kaua’i on the cheap. If you’re really broke, hitch-hiking is quite common. I picked up many hitchers, and even had to do it a couple of times myself.